?B/07 
.57 



1*30 



LIBRARY OF CONGRESS 






KlllillllOlll 



003 591 847 4 



Hollinger Corp. 
P H8.5 



DIRE 



FOR 



REGULATING, USING AND TAKING CARE 



CHRONOMETERS, 

ON SHORE AND AT SEA. 

TOGETHER 

WITH FORMULAS FOR WORKING THE TIME AND 
APPLYING THE ERROR AND RATE. 



By DANIEL STANSBURY. 



NEW-YORK: 
E. & G. W. BLUNT, 154 WATER-STREET. 

G. F. Bunce, Printer. 

1830. 



SOUTHERN DISTRICT OF NEW-YORK, ss. 

BE IT REMEMBERED, That on the 16lh day of August, A. 
D. 1830, in the fifty-fifth year of the Independence of the United 
States of America, E. &G. W. BLUNT, of the said district, hath 
deposited in this office the title of a book, the right whereof he 
claims as proprietor, in the words following, to wit : 

' 4 Directions for regulating, using and taking care of Ohronometers, on shore 
and at sea, together wiUi Formulas for working the time and applyiug the error 
and rate. By Daniel Stansbury." 

In conformity to the Act x>f Congress of the United States, entitled " An Act 
for the encouragement of Learning, by securing the copies of Maps, Charts, and 
Books, to the authors and proprietors of such copies, during the time therein 
mentioned." And also to an Act, entitled " An Act, supplementary to an Act, 
entitled an Act for the encouragement of Learning, by seouring the copies of 
Maps, Charts and Books, totfte authors and proprietors of such copies, during 
the times therein mentioned, ami extending the benefits thereof to the arts of 
designing, engraving, and etching historical and other prints." 

* FRED. J. BETTS, 

Clerk of the Southern District of Netc-York. 



1 



PRELIMINARY REMARKS. 



The easiest and most convenient of all the methods at present 
known, of finding the Longitude at sea, is by the use of a time-keeper; 
it is however, an instrument that is subject to man)* casualties, and of 
course requires a good deal of care ; its error for Greenwich time as 
well as its rate of going ought to be carefully ascertained before you 
leave the land, and the Longitude by Chronometer compared after- 
wards, as opportunities may occur, with the situation of headlands or 
other objects, whose Longitudes are known; Also, by frequently com- 
paring the Greenwich time as shown by Chronometer, with that found 
from Lunar distances as hereafter directed, the danger of depending 
upon the Chronometer will be much diminished. 

The uniformity of the motions of Chronometers is liable to be af- 
fected more or less by changes in the state of the atmosphere, notwith- 
standing the great degree of perfection arrived at by the artists in 
constructing them upon principles calculated to counteract the effects 
of those changes. Therefore, the Navigator's confidence in the Lon- 
gitude deduced from his Chronometer, will be in proportion as he ascer- 
tains, by a long series of observations, that its rate of going is uniform 
during voyages through various climates ; or if changes in the rate do 
happen, that the error resulting therefrom, may be accounted for and 
corrected by equations, depending upon the height of the Thermome- 
ter and Barometer. A good time-keeper is also a very valuable assis- 
tant, for finding the elapsed time between observations, and particu- 
larly for connecting Lunar distances, taken w r hen the time under the 
meridian of observation is not well known, with altitudes taken either 
before or afterwards to ascertain the time. 

E. & G. W. BLUNT have erected an Observatory, and procured 
a first rate pendulum time-keeper, which they have taken great pains 
to ascertain goes uniformly, and offer their services to gentlemen, who 
may desire to have the error and rate of their Chronometers accurately 
known; every attention will be paid to this part of their business, 
since they are aware, that the instrument can be of little use to a Navi- 
gator, if he should be deceived by the persons who undertake to do 
this business for him. 

Nevertheless, every Navigator who uses a Chronometer, should pro- 
vide himself with an artificial horizon, in order to be able to ascertain 
its error and rate, as nearly as possible with his own instruments, as he 



may frequently happen in ports and places, where such assistance as 
is now offered cannot be obtained, and no opportunity should be lost, 
either on shore or on ship-board, whenever the Longitude of the place 
is correctly known. 



TO FIND THE ERROR AND RATE OF A CHRONOME- 
TER WITH AN ARTIFICIAL HORIZON. 

(1.) In the morning, or afternoon, when the Sun is rising or falling, 
fast* observe a set of three, four or five angles between the lower 
limb of the Sun, and the near limb of its reflected image in the arti- 
ficial horizon, having an assistant to note with care the exact time per 
Chronometer of each observation, half the mean of the angles will be 
the altitude of the Sun's lower limb, and the mean of the times shown 
by the Chronometer, will be the Chronometer time of such altitude. 

(2.) The altitude of the Sun's lower limb must be first corrected 
by adding the Suns semidiameter from page III of the Nautical Al- 
manac. Then take the refraction corresponding to the altitude, from 
tab. xii. [Bowditch] and when great accuracy is required, correct it 
for the height of the Thermometer and Barometer, from Table xxxvi ; 
also subtract from it the Sun's parallax in altitude from Table xiv, the 
refraction so corrected must be subtracted from the Sun's altitude, the 
remainder will be the true altitude. 

(3.) There is no dip to be allowed for. If there be any index error 
H must be applied to the whole angle, or only half of it to the alti- 
tude. 

(4.) If the Chronometer error be not known, the Greenwich time 
must be computed by adding the west longitude (in timet) to the ap- 
parent time at the place of observation, or by subtracting the east lon- 



* The best time to observe the altitude of any celestial body is when it bears 
east or west, if it be then high enough, as any error in the latitude, the declination 
or even the altitudes has the least effect upon the computed time, therefore this posi- 
tion is to be preferred, if the object be at least 5 or 6 degrees high ; but because 
there is an uncertainty, as to the exact quantity of refraction, an object should not 
be too near the horizon, for there is danger that the advantage of the position will 
be more than counterbalanced by an error in the refraction. In very high latitudes, 
care must be take that the object be not too near the meridian, even if at a less alti- 
tude than 5 or 6 degrees. When the latitude is of the same name, but less than the 
declination, the object will not be east or west at all; in this case seek that place in a 
traverse table, where the degrees of declination are found in the distance column, 
and the degrees of latitude in the departure column ; the corresponding course 
will be near to the best altitude for finding the time. 

t The longitude may be reduced from degrees, and minutes to hours, minutei 
and seconds by Tab. xxi. 



gitude. At subsequent observations, vvlie n the Chronometer error is 
known, the Greenwich time may be inferred more easily from the 
Chronometer. 

(5.) Astronomers commence their day at the noon of the given day 
of the month, and count the 24 hours of that day in succession to the 
the next noon, this method is used in all problems for finding the 
longitude ; therefore the civil time and Astronomical time are the same 
from noon to midnight, after which Astronomers count the hours from 
12 to 24 of the same day, and the civil time commences another day 
at midnight, thus the 21st July at 7, A. M. civil time must be written, 
20th July, 19 hour, Astronomical time.* 

(6.) Take from page II of the Nautical Almanac, the Sun's declina- 
tion for the nearest noon, also its daily variation, then say as 24 hours 
or 1440 minutes, is to the difference of the Greenwich time from noon, 
so is the daily variation to the correction of the declination, to be ad- 
ded if after Greenwich noon, or subtracted, if before noon, when the 
declination is increasing ; but to be applied contrarily when the declina- 
tion is decreasing. 

(7.) But an easier and in most cases a sufficiently exact way of find- 
ing the correction to the declination, is by Tab. v. Find the time from 
Greenwich noon in the top column under which, and opposite to the 
day of the month, in one of the side columns stands the correction, which 
must be added or subtracted according to the direction that stands on 
the top of the column where the day of the month is found. 

(8.) Having obtained the reduced declination ; if it be of a differ- 
ent name from the latitude, add it to 90° ; or if it be of the same 



* It will be sometimes convenient to write the days as well as the 
hours, minutes and seconds ; because in adding the longitude to 
the time it may exceed 24 hours, when one must be carried to the 
days, or in subtracting, if the longitude exceed the time at the place 
of observation, 24 hours must be borrowed and the days written one 
less, thus for example at lOh. 9m. 10s. A. M. of the 24th civil day, 
write d.1h. m. 

Time at ship 23 22 9 10 

AddW-Lon. intime 3 1 30 



Greenwich time 24 1 10 40 

Again, in east longitude at 3h. 26m. 42s. P. M, of 19th civil day, 
we may write 19d. 3h. 26m. 42s. 

Sub. East loii£, in time 5 9 15 



Greenwich time 13 22 17 27 



name subtract it from 90° ; the sum or difference will be the polar 
distance. 

(9.) Add together the Polar distance, the latitude of the place of 
observation, and the Sun's true altitude ; from half the sum subtract 
the altitude and note the remainder. 

(10.) Add together the log-cosecant*, of the Polar distance, the log- 
secant of the latitude, (rejecting the ten in each index,) the log-cosine 
of the half sum, and the log-sine of the remainder ; seek for half of 
the sum of these four logarithms on Tab. xxxvii. among the log-sines 
in the corresponding side column will be found the time ; or if not 
found exactly, it must be taken out to the nearest second by propor- 
tion. 

(11.) Having thus found the apparent time at the place observation, 
take from the Nautical Almanac, page 11, the equation of time pro- 
portioned for the Greenwich time, (4) and apply it to the apparent 
time, according to directions at the top of the column, and the result 
will be the mean time at the place of observation. 

(12.) Apply the Longitude (in time) to the mean time at the place 
of observation, by adding it if east, or subtracting it if west, (4) and 
the result will be the mean time at Greenwich. 

(13.) The difference between the mean time at Greenwich thus 
found, and the time of observation shown by the Chronometer, will be 
its error, which is additive if the time shown by Chronometer, be 
less, or subtractive, if it be greater than the mean time at Greenwich. 

(14.) These observation ought to be repeated as often as practicable 
and as long as the time-keeper remains in port. After a series of ob- 
servations, t note whether the error increases or diminishes, and if so 
how much ; divide the number of seconds it has increased, or dimin- 
ished by the number of days in the interval, and the quotient will be 



* The Log-cosecant of the Polar distance is always the same as the Log-secant of 
of the declination. 

t It is better to compare the morning observations with each other, and afternoon 
observations with each other, because any unavoidable errors in the instrument, the 
horizon, or the refraction, will generally produce the same effect each morning and 
each afternoon ; therefore a series of observations ought to be made with the same 
instrument, and if a glass horizon be used, with the same edge of it toward the ob- 
server, for fear that the surfaces may not be exactly parallel. Thus suppose an 
error in the morning altitude to give five seconds too little, the same, error in the 
afternoon altitude will give five seconds too much ; if these morning and afternoon 
observations were compared together, a watch that kept true time, would appear to 
have lost 10", whereas, if the same error were repeated next morning, the eame 
watch would be right. 



the rate ; if there be a number cf intervals take the mean of the several 
quotients for the rate. 

(15.) At any subsequent time the error may be discovered by multi- 
plying the rate by the number of days since the error was last found, 
-2nd adding the product to that error if it be increasing, orsubtracting if 
it be decreasing — 

EXAMPLE I. 

In the city of New- York, in Lat. 40° 42' N. and Long. 74° W. 
at about 20 minutes past 7 o'clock, on the 31st July, 1831. The fol- 
lowing angles between the near limbs of the Sun, and its reflected 
image, in the artificial horizon, at the following times per Chronome. 
ter being given, required the error for mean Greenwich time. For 
Thermometer 80°, and Barometer 29 70. 

h. m. s. 
Time per Chronometer 1. 20. 10 
1.21. 5 
1.21.50 
L22.40 
1.23. 7 



Mean 



5) 108.52 
1.21.46 

d. h. m. s. 
Time per watch (5) 30. 19. 20. 
Long. New-York 4. 56. 



Green, time ..... 31. 0.16.0 

^'sdec.31 JulyperN.A.18. 25. 10 
Correction for 16' tab. v. Sub. 10 



Reduced declination N. 18. 25. 
90. 



Angles , 



52. 28. 45 
52.50*15 
53. 8.30 
53.27.30 
53.46.45 



5)265,41.45 

Mean angle 53. 8. 21 

Half =alt L. limb ... 26. 34. 10 
Add © semidianeter N. A. 15. 47 



© apparent altitude . . 26. 49. 57 



Refraction tab. xii. 1.52 
Cor. tab.xxxvi. sub. 8 
^parallax tab. xiv.sub . 8 



®'s true alt. 



0. 1.36 
26.48.21 



Polar distance 71. 35. 

Latitude N. 40.42. 

Sun's true alt 26.48.21 



Co-secant.... 0.02283 
Seeant 0.12025 



Sum ? 139. 5.21 

Half sum 69.32.40 Cosine, 

Remainder 42.44.19 Sine .. 



Time corresponding in cols, 
marked A. M. 7h. 19m. 38" 



Sum. 
Half, 



. 9.54343 
.9.83165 

19.518J6 
.9.75908 



8 

1). m. s. 
Which is Astronomical time (5) July 30. 19. 19. 38 
Equation of time per N. A. add 6 . 4 

Mean time at New- York, 30. 19. 25 . 42 

Longitude of New- York, W 4. 56 . 

Mean time at Greenwich, 31. 0.21. 42 

Time per Chronometer 1. 21. 46 

Chronometer error . . fast 1 . . 04 



Again, at the city of New-York, in the morning of the 9th August 
1831, the following angles between the lower limb of the Sun and the 
near limb of its reflected image, in the artificial horizon being given, 
together with the following times per Chronometer, required its error, 
for Therm. 70 Bar. 29. 30. 



Times per Chron 1. 27. 10 

1.27.45 
1.28.32 



Mean 



3) 83.27 

1.27.49 

h. m. s. 
Error 31st July, 1.0. 4 
Estimated rate 5. ) 1. 12 
per day increasing $ — — 1 . 1. 16 

Estimated Green, time. 0, 26. 33 



Declination at noon . 16. 1. 35N. 
Corr. for 27m. tab. v. sub. 21 



Reduced declination . . 16. 1.14 
90. 



Angles . 



..51.40.30 
52. 0.45 
52. 19. 15 



3)156. 0.30 

Mean 52. 0.10 

Half 26. 0. 5 

© S. D. per N. A. add 15. 49 



® app. altitude 26. 15. 54 

Refraction tab. xii. 1. 55 
Corr. tab. xxxvi. sub, 7 
© par. tab. xiv. sub. 8 



1.40 



@'strue alt. 



26. 14. 14 



Polar distance 73.58. 46 

Latitude 40.42. 

True altitude 26. 14. 14 

Sum 140.55. 

Half sum 70.27.30 

Remainder 44. 13. 16 

Time corresponding in cols. > 
marked A. M. 7h. 24m. 20s. $ 



Co-secant.... 0.01720 
Secant 0.12025 



Cosine 9. 52439 

Sine 9.84350 

Sum 19. 50534 

Half 9.75267 



9 

d. h. m. 9. 

Astronomical time, Aug 8. 19. 24. 20 

Equation per N. Ai add 5. 17 

8.19.29.37 
Longitude New- York, W .... 4.56. 

Mean time at Greenwich 9. 0. 25. 37 

Time per Chronometer 1.27.49 

Chronometer too fast 1. 2-12 

too fast 31st July 1. 0.4 

Error increased in 9 days 0. 2. 8 

128 s. divided by 9 quotes 14. 2 seconds per day. 

Also on the 15th of August, about the same time in the morning, by 
similar observations, the Chronometer appeared too fast. h. m. s. 

1.3. 3 
Too fast on 9th August 1.1.40 

Gained in 6 days 1.23 

83 s. divided by 6 quotes 13. 8 
former quotient 14. 2 

28. seconds per day. 
Mean rate 14. 

TO FIND THE LONGITUDE BY A CHRONOMETER. 

(16.) Take a set of altitudes of the sun's lower limb, or of a star,* 
when nearly east or west, (1 ) note the time of each alti- 
tude per Chronometer and take the mean of the altitudes and the 
times. 

(17.) Bring the Chronometer error forward to the time of observa- 
tion ; in order to do so, multiply the number of days since it was last 
found by the daily rate, and add the product to the former error, if it 
were increasing, or subtract it if decreasing ; this sum or difference 
will be the present error which must be applied to the mean of the 
times shown by the Chronometer, by addition when the Chronome- 
ter is too slow, or by subtraction when it is too fast, and you will then 
have the mean time at Greenwich. (15.) 

* A bright star taken in the twilight, or any time when the horizon 
is well defined, is better than to take the sun when too near either the 
horizon or the meridian, more especially if the latitude be not exactly 
known, 

2 



10 

(18.) The altitude of the sun's lower limb, must be corrected by ad 
ding to it of the semidiameter. (from the Almanac) and the paralax 
(from table xiv.) Also by subtracting from it the refraction* (from 
table xii.) and the dip (from table xiii.) the remainder will be the 
sun's true altitude. 

(19.) As a star has neither semidiameter nor parallax, it is only 
necessary to subtract the dip and the refraction to obtain the true 
altitude. 

(20.) Take out the sun's declination from the Almanac, correct 
it as before, (6.) and find the polar distance ; with these, and the lati- 
tude, find the apparent time at the place of observation as in the pre- 
ceding examples. 

(21.) Take from the Nautical Almanac, the equation of time pro- 
portioned for the Greenwich time, and apply it to the apparent time, 
according to directions at the top of the column, the result will be the 
mean time at the place of observation. t 



* It will be seldom necessary to notice the variation in refraction 
for the state of the atmosphere, unless the object be very low, or you 
are finding the rate of your Chronometer, or have other cause to re- 
quire great precision. 



Specimen of a table 
for ten davs in March 
1631. 



Day 



Error. 



Diff. 



t It is easier in practice and has the advan- 
tage, if great accuracy should be required, to 
apply the equation to the Chronometer with a 
contrary sign, and find the apparent time at 
Greenwich, since the declination is given in the 
Almanac for apparent time. 

A small table may be made at leisure times, 
containing the Chronometer error for each day, 
up to the usual hour of observing, for a month or 
more a-head ; the equation for each day, up to 
the same hour, may be incorporated with the 
error, so that both may make a compound quan- 
tity, to be added or subtracted from the Chro- 
nometer at each observation ; this quantity may 
be easily proportioned to any other part of the 
day or night : the sum or difference of the daily 
rate and the daily variation of equation, as given 
in the Nautical Almanac, will be the daily dif- 
ference of the compound quantity ; these daily differances being con- 
stantly added to or subtracted from it, for a month or any other 
given time ; if the result corresponds with the sum or difference (as 
the case may be) of the Chronometer error and the equation, at the 
same hour of the day at the end of the time, it will afford a strong 
presumption that the table is right for each intermediate day. 



H. M. S. I S. 

1.23.20.0 on R 
1.23.40,6;^ 

1.24.23.1 ii° 
1.24.45,1.^, 

-, Q^ Jr 22.4 

1.2a. /,o o rt 
1.25.30,2^3^ 

1.26.17,0 .^'X 



1.26.40,9 



23.9 



11 

(2*2. ) The different of the meant time at the place of observation, 
and the mean time at Greenwich found by Chronometer, is the 
longitude in time, which will be west if the Chronometer time be 
greater, or east if it be less. 

(23.) The longitude in time may be converted into degrees by table 
xxi. or by reducing it to minutes and seconds, and dividing it by 4, 
the quotient will be degrees and minutes, and the remainder will be 
quarters of minutes. 

24. Chronometers usually show the time for 12 hours only, there- 
fore care must be taken to designate which twelve hours refer to noon 
and which to midnight ; the hours after midnight must be increased 
12 : thus 8 o'clock in the morning must be written 20 hours of the 
preceding day. (5.) 

Example I. 

At about half past 8 o'clock, A. M. on the 25th Feb. 1831. in lat. 
32° 10' S. observed the following altitudes of the sun's lower limb, 
and noted the respective times by a Chronometer, whose error for 
mean Greenwich time, brought to 8 o'clock in the morning of the 23d 
instant, was 2h. 34m. 50s. additive, and was increasing by a daily 
rate of 18.5s. the height of the eye 22 feet from the sea ; required the 
longitude of the place of observation. 



Times per Chro. 



D. H. M. f. 

24.15.42.23 
42.45 
43.13 
43.38 
44. 



Altitudes L l. 



o t it 

37.25.50 

37.30.40 

37.34.20 

37.40.30 

37.44.50 



5) 
Mean. 

Error 23 inst. add 
Two day's rate add . 


215.59 

15.43.12 

2.34.50 

37 


Mean : 5) 176.10 

37.35.14 

16.11 

Sunspar.tb. xiv. 7 


Mean Greenwich time . 


18.18.39 


37.51.32 
Dip. tab. xiii. 4.37 
Ttefrac. tab. xn. 1,14 

— 5.51 



Suns true alt. 



37.45.41 



12 



© dec. 25h. noon 
Cor. tal. V. 5h. 58m. 
before noon add 



Polar distance. 

Lat. 
True alt. 



9.14.50 



. 5 5.18 


9.20. 8 
90 


80.39.52 
32.10. 
37.45.41 



..Co-secant. 0.00579 
Secant. 07237 



Sum . . . 150.35.35 ....Co-sine . 9.40453 

Half sum . . 75.17.46 Sine. 9.78479 

Remainder . . 37.32. 5 

Sum. 19.26748 

Time corresponding from col. \ half Q 63374 

marked, A. M. 8h. 36m. 7s. ) 
Eqnat.N.A.add 13 24 

8 49 30 



H. M. S. 

20.49.36 

18.18.39 



Astronomical mean time at ship. 
Mean time per Chronometer. 

Longitude in time. . . : • 2.30.57 

150m. 57s. divided by 4 gives 37° 44' ^ longitude, which is east be- 
cause the Chronometer time is less. (22. 23.) 

25. When a star's altitude is observed and corrected for dip. and 
refraction, (20) take its right ascension and declination from table viii. 
or its right ascension and north polar distance from the N. A. page 174 
&c. bringing them down to the time of observation, by applying the 
annual variations as directed — that is, multiplying the annual variation 
by the number of years elapsed since the catalogue is dated, and ad- 
ding or subtracting the product, according as the sign -f- or — is an- 
nexed to the variation ; if the declination be taken from table viii. add 
it to 90° or subtract it from 90° accordingly as it is of a different name 
or of the same name as the latitude (8.) But when the North Polar 
distance is taken from the Almanac, if you should be in north latitude 
it will be right, but if you should be in South latitude subtract it from 
180° and the remainder will be the Polar distance to be used in 
finding the time. 

26. With the Polar distance of the star, the latitude of the place, 
and its true altitude compute the meridian distance as the afternoon 
time would be computed from an altitude of the sun. (10.) 

27. When the star is west of the meridian, add its meridian dis- 



13 

tance to its right ascension; when it is east, of the meridian, subtract 
its meridian distance from its right ascension (increased 24 hours if 
necessary to make it the greater,) the sum or difference will be tho 
right ascension of the meridian. 

(28.) Correct the Chronometer time of the Stars altitude for its error 
brought to the time of observation. (17.) 

(29.) Take the Sun's right ascension, and its daily variation from the 
Nautical Almanac, page II, and proportion it to the Greenwich time of 
observation, which may be done by table xxxi ;* subtract it from the 
right ascension of the meridian, (increased 24 hours, if necessary to 
make it the greater) and the remainder will be the apparent time at 
the place of observation, which reduce to mean time by applying the 
equation from the N. A. (21.) 

(30.) The difference between the mean time at the place of obser- 
vation, and the mean time at Greenwich will be the Longitude in 
time, (22) (23). 

Example II. 

In the evening of 1st March 1831, in Lat. 23°. 20'. S. observed the 
following altitudes of the Star Aldebaran's west of the meridian, and 
noted the respective times, per Chronometer, the height of the eye 
being 22 feet from the sea, required the Longitude. 

h. m. s. 
Times per Chronometer 4. 47 . 40 Altitudes of Aldebaran 17. 11 . 
4.48.11 17. 6. 

4.48.51 17. 3. 

4.49.22 16.57. 

4.49.56 : 16.48. 



5) 244. 5)85.5. 

Mean 4.48.43 Mean 17. 1.0 

Error 25 Feb. add .... 2. 35. 25 Dep. table xiii. 4'. 37" 

t 4s days rate a 181s. add 1.23 Refrac. tab. xii. 3. 5 



Mean Green, time 7.25.36 



7.42 



* 's true altitude .... 16.53.18 



* When the Greenwich time is used, you have nothing to do with 
the Longitude in the right hand column of the table. 

t Since the rate is the variation in 24 hours from the mean time, it 
ought in strictness, to be applied to each 24 hours of mean time, rather 
than to each natural day at ship, because the latter are longer or shorter 
as the ship makes west or east longitude, when the difference amounts 
to some seconds, it may be allowed for. 



14 

tt. M. S. 

Aldebaran'sdec.tab.viii. Jan. 1st 181016°. 7. ON. R.Ascen. 4.25.1 
21 years 2ms. ann. var. a8.2s. + 2.52 Var at3.42+ 1. 12 



add 90° P. D. 



... 106.9.52 



4.26.13 



OR, 



Aldeb.N.P.dist.perN.A.Jan.1.1825 73.51. 2 R. Aseen. 4.25.53 
6 years 2ms. ann. var. a 7.7 Sub 47 a 3.43 21 



73.50.15 

180. 



4.26.14 



Aldebaran's Polar distance 106. 9. 45 

Latitude 23.20 

5fc true altitude 16.53.18 

Sum 146.23. 3 

Half sum 73.11.31 

Remainder 56.18.13 

Time corresponding in column P. M. } 

=>k's Meridian distance 4h. llm.53 5 

Aldebaran's R. Ascension ...... 4 . 26 . 14 



Sum R. Ascension of Meridian 8. 38. 
Increase it (29) 24 



Cosecant 0.01751 
Secant 0.03706 



Cosine 9.46114 
Sine 9.92012 



Sum 19.43583 
iSum 9.71791 



Sun's right Ascension Green, noon 1st March N. A. h. m. s. 

22.46.55 
Corr. for7h. 12m. Green, time tab. xxxi. for daily 

variation 3m. 44s. 5 add 1. 7 



32.38. 7 



22.48. 2 



Apparent time at ship 9.50. 5 

Equation from N. A. add 12.39 

Mean time at Ship 10. 2.44 

Meantime per Chronometer 7.25.36 



Longitude in time (22 &23) 2.37. 8 

m. s. 

4)157. 8 

Longitude in degrees .......... 39° . 17 



TO REGULATE A CHRONOMETER AT SEA. 
(31.) There seems to be no better method at sea of knowing whether 
the Chronometer shows the correct Greenwich time, than by fre- 
quently comparing it with that derived from lunar distances. 



15 

(32.) In order to do so, note the time by Chronometer of the lunar 
distance, apply the error brought forward to the time of ebserva- 
tion, and the equation of time with a contrary sign, (17, 18.) so as to 
obtain the apparent time at Greenwich; the difference between which 
and the apparent time at Greenwich, found by the lunar distance, 
will be the difference of longitude (in time) between the Chronome- 
ter and the lunar distance, which ever is greater, gives the Ship's place 
so much to the westward of the other : this will be all that is necessary 
at the time, — it is generally lost labour to compute the time from alti- 
tudes taken with the distances, if the time be noted by a Chronome- 
ter. 

(34.) Once a day, or as often as the sun or star is in a proper position 
and visible, and the horizon well defined, take a set of altitudes, com- 
pute the time at Ship, and compare it with Greenwich time by the 
Chronometer (Ex. i.) in order to know the longitude by Chronometer, 
then will the longitude by the lunar be also known, (32.) which will 
be the place of the Ship, at the time when the altitude was taken.* 

(33.) By constantly, or as often as opportunities occur, comparing 
the Chronometer with the Greenwich time derived from the lunar dis- 
tances, if the Navigator has a good instrument, is careful in using it, 
and in making his computations, he will be able to know what depen- 
dence he can place on the going of his Chronometer, since the mean 
result of a great many distances of objects to the east and west of the 
moon, carefully taken and computed, and all thus connected together 
by the Chronometer may be supposed to be a near approximation to 
the truth. 

(35.) Should the Chronometer stop, or runjdown, observe what time 
it stands at ; if you are to the eastward of your first meridian, add the 
estimated longitude to it, or if to westward subtract it ; the sum or diff- 
erence will be the time at ship, when the chronometer may be wound 
up or set a going, in order thather error may be as small as possible. 

* Demonstration. Suppose exactly at midnight, the apparent time 
at Greenwich per Chronometer to be lOh. lm. and that deduced from 
the lunar to be lOh. 2m. the lunar will give the Ship lm. or 15 miles 
west of the Chronometer, because as the time is supposed to be exact- 
ly midnight, the longitude by Chronometer will be lh. 59m. or 29° 45' 
east and that by lunar lh. 58m. or 29° 3CTeast ; again, suppose in the 
morning after the Ship had made 4m. or 1° more easting, the longitude 
deduced from an altitude of the sun and the Chronometer will be 
2h. 3m. or 30° 45' east, then will the longitude of the Ship per lunar 
be 2h. 2m. or 30° 30' at the same time, because you must add the run 
of the Ship to the longitude she was in at midnight. 



16 

36. Having set the chronometer a going, at the first opportunity take 
several sets of distances between the Moon and the Sun, and the Moon 
and the Stars to the eastward and westward of her, with their respec- 
tive altitudes, noting the time of each per chronometer ; compute the 
true distance, and thence the apparent time at Greenwich or other 
first meridian, of the respective distances, to each of which apply the 
equation of time from the Nautical Almanac, according to the direc- 
tions at the top of the column ; the result will be the mean times of 
the respective distances at the first meridian, the difference between 
which, and the times noted by the chronometer when the distances were 
taken, will be the chronometer's error — additive, if the chronometer's 
time be less than that shown by the lunar — otherwise, subtractive. 

(37.) The mean error found from any number of observations made 
in the course of 24 hours may be taken for the error at the middle time, 
or add together the times of each observation, and the errors found at 
each time, and divide the sums by the number of times — the quotients 
will be the time the error may be reckoned from, and the mean error. 

(38.) The rate of the chronometer may be supposed not to be mater- 
ially changed from the circumstance of its stopping, or running down ; 
but lest it should, repeat the same observations several days after- 
wards, and note whether the chronometer has gained or lost, and if so, 
how much ; also note the exact interval between the mean time the 
error was found at the [first and the second set of trials. Divide the 
gain or loss of the chronometer by the interval of time — the quotient 
will be the rate or daily gain or loss ; if the interval of time be reduced 
to days, and decimals of days, and the gain or loss reduced to seconds, 
annex as many ciphers to the seconds as will give them one more de- 
cimal place than the days have, and the quotient will be seconds and 
tenths. 

(39.) In order to reduce hours and minutes to decimal parts of a day, 
reduce them first to minutes, annex any number of ciphers, and divide 
by 144; the quotient will be the decimal parts of a day, and must con- 
tain one more figure than there were ciphers annexed ; if it does not, 
prefix ciphers to it to make it so. 



EXAMPLE. 

On the 21st of May, 1820, in longitude by account 90° 4' east of 
Greenwich, the Chronometer run down, and stood at 30m. 8s. past 

Add the longitude by account in time, 6 16 

I wound up the Chronometer in the evening, > 
when the time at ship was, J t> o0 24 

During the night I took six sets of distances and altitudes, from 
which I obtained the following results, viz. : 

h. m. s. h. m. s. 

44 50 Time per Chronometer, 44 50 

h. m. s. 
Greenwich time per J) & Antares, 50 17 
Equa. per Nautical Almanac Sub. 3 44 



46 33 m. s. 
1 43 



1 15 25 Time per Chronometer, 1 15 25 

Greenwich time per 2> & Pollux, 1 21 2 
Equa. per Nautical Almanac Sub. 3 44 



1 17 18 

1 53 



10 Time per Chronometer, 2 10 

Greenwich time per ]) & Pollux, 2 5 26 
Equa. per Nautical Almanac Sub. 3 43 



2 1 43 
2 33 

3 30 20 Time per Chronometer, 3 30 20 

Greenwich time per X) & Antares, 3 35 40 
Equa. per Nautical Almanac Sub. 3 43 

3 31 57 

— 2 37 

4 12 Time Per Chronometer, 4 12 

Greenwich time per D & Antares, 4 5 10 
Equa. per Nautical Almanac Sub. 3 43 

4 1 27 

1 15 

5 1 16 Time per Chronometer, 5 1 16 

Greenwich time per j> & Antares, 5 7 
Equ. per Nautical Almanac Sub. 3 43 

5 3 17 

— 2 1 



18 

On the following day; I took five sets of* distances between the 

Sun and Moon, from which I obtained the results noted below — viz. : 

h. m. s. h. m. s. 

20 49 18 Time per Chronometer 20 49 18 

Greenwich time per D and Sun, 20 54 34 

Equa. per Nautical Almanac, 3 40 

20 50 54 m. s. 

1 36 

2130 -2 Time per Chronometer, 2130 2 

Greenwich time per ]) and Sun, 21 35 44 
Equa. Nautical Almanac, 3 40 

21 32 4 

2 2 



22 5 26 Time per Chronometer, 22 5 26 

Greenwich time per D and Sun, 22 10 31 
Equa. per Nautical Almanac, 3 40 

22 6 51 



22 33 14 Time per Chronometer, 22 33 14 

Greenwich time per D and Sun, 22 38 30 
Equa. per Nautical Almanac. 3 40 

22 34 50 

23 13 50 Time per Chronometer. 23 13 50 

Green, time per D and ©,23 19 20 
Equation per Nautical Al. 3 40 

__ 23 15 40 



1 25 



36 



150 



5)110 11 50 
22 2 22 

2 45 22 



5)8 29 
Mean result of five distances, Chro. slow, 1 41.8 

Last night mean result 6 dis. Chro. slow, 1 40.3 



2) 24 47 44 2)3 22.1 

12 23 52 Mean result last night and to-day, 1 41.05 

From the preceding trials I found that the Chronometer was slow of 
mean Greenwich time 1m. 41s. on the 21st May, at 12h. 23m. 52s. 
Chronometer time. 

Again, on the 2d of Jui?e, I made another trial by six sets of distan 
tances between the Moon and Stars to the eastward and westward of 
her ; and five sets between the Sun and Moon ; the mean result of 
which was, that the Chronometer was slow of Greenwich time 3m. 
22.75s. on the 2d of June, at 18h. 13m. 5s. Chronometer time. 



19 



b. in. h. s 

The 1st trial May 21, 12 24 Chro. slow, 1 41.05 

The 2d trial, June 2, 18 13 Chro. slow, 3 22.75 



Difference, 12 5 49 1 41.7 

Now to the fractional part of a day, 5h. 49m or 349 minutes, annex 
two ciphers, and divide by 144; (30) the quotient is 243; hence the 
elapsed time between the trials is 12 243 days, which divide into lm, 
41. 7s. or 101.7000s. the loss of the Chronometer in this interval ; the 
quotient is 8.4s., its daily rate of losing. 

It is probable that fewer observations might answer, but since the 
accuracy of the error and rate will be in proportion to the number, and 
the correctness of them; if the weather be good, and the course of the 
ship such that there be no necessity of taking in any of the sails to ob- 
tain them, I should prefer to have at least as many as I have given the 
result of in the preceding examples. 



DIRECTIONS, REMARKS, &c. 

1. Be careful, when carrying the Timekeeper to and from the Ship, 
to secure the Gimbol by the Stay, to keep it steady ; and by all means 
avoid giving it quick circular motion. 

2. Chronometers should be so placed as to be as little as possible ex- 
posed- to sudden shocks, from the sea striking the ship, or from the 
shutting of doors, &c. They ought not to be exposed to a current of 
air. — Nothing magnetic should be allowed near them. 

3. When on board, free the Stay, let it swing horizontally, and place 
it secure and as little disturbed as possible during the Voyage. Ship- 
time, for Deck Observations, is recommended to be obtained by a 
Watch, comparing it with the Chronometer, before and after the ob- 
servation. 

4. In winding, turn it over gently ; put the Valve back, apply the 
Key, turn easy, and avoid sudden jerks. 

5. Pocket Chronometers must be held immoveable in one hand 
whilst winding with the other, to avoid circular motion, which may 
not only alter the Rate, but injure it. 

6. If it should happen to be let down or stop, it must, when wound 
up, have a quick circular motion in the plane of the Dial to set it 
agoing. Never touch the Hands to set the Chronometer, but wait till 
the Time arrives at which they point. Be regular in winding. 



CHRONOMETER RATE. 



Date. 



Mean 
Rate. 



Diff. for 

Green.time. 



Remarks. 



Time 


per 

H. 


Chronometer 
M. s. 


$'s Altitude. 


3) 




: 


: 


3) : 


Mean 
Correction 


Mean. : 
Semidiam Par. + 


Time at G. 


o 


/ 


u 


®'s App. Alt. 
Dip. Ref. 


©'s dec. noon 
Varia. 


#'s Cor. Alt. : : 


Declin. 
Polar Dist. 




: 


: 




©'s cor. alt. 
Lat. 
Polar dist. 

Sum. 


Q 


/ 


n 


Secant. 

Co. Secant. . 


Half Sum. 
©'s alt. sub 




: 


: 


Co. Sine. 


Remainder. 




: 


: 


Sine. 


Appar. time. 
Equation. 


H. 


M. 


s. 


2) ' 
Sine. = ' 


Mean time at 
Ship. 
atG. 




: 




O ' " 


Long, in Time. 




J 


; 





Time 


per Chronometer. 

H. M. s. 




Altitude. 


3) 




3) 




Mean, 
Correction 


: 


Mean. 
Semidiam Par. 


+ 


Time at G. 


O ' " 


m A PP . Mt. 

Dip. Ref. 
@'s Cor. Alt. 

Secant. 

Co-Secant. 


j • 


@'s dec. noon 
Varia. 


: : 


Declin. 
Polar Dist. 






g^s cor/alt. 
Lat. 
Polar dist. 


O ' " 




Sum. 






Half Sum. 
Hi's alt. sub. 

Remainder. 


H. M. S. 


Co. Sine. 

Sine. 

Sine. = 








Appar. time. 
Equation. 

Mean time at 
Ship. 
atG. 


o ' " 


Long, in Time 


: : 


= 





Time 


per < 
ii. 


Chronometer 

M S. 


l Altitude. 

O ' // 


3) 








3) : 


Mean 
Correction 


: 






Mean. : : 
Semidiam Par. + 


Time at G. 


o 


f 


it 


®'s App. Alt. 

Dip. Ref. : : 


©'s dec. noon 
Varia. 


© f s Cor. Alt. 


Declin. 
Polar Dist. 






: 




©'s cor. alt. 
Lat. 
Polar dist. 

Sum. 


o 


I 


n 


Secant. 

Co. Secant, . 


Half Sum. 
©'s alt. sub 


: 




: 


Co. Sine. 


Remainder. 


H. 






Sine, ' 


Appar. time. 
Equation. 


M. 


s. 


2) ' 
Sine. = ' 


Mean time at 
Ship, 
at G- 






: 


o • tf 


Long, in Time. 




| 


• 





Time per Chronometer 
h. m. s. 



©'» Altitude. 



3) 



Mean. 
Correction 

Time at G. 



@'s dec. noon 
Varia. 



3) : 

Mean. 

Semidiam Par. + 



© App. Alt. 
Dip. Ref. 

@'s Cor. Alt. 



Declin. 
Polar Dist. 



®'s cor. alt. 
Lat. 
Polar dist. 

Sum. 

Half Sum. 
© ? s alt. sub. 

Remainder. 



Appar. time. 
Equation. 

Mean time at 
Ship. 
atG. 



....Secant. 
...Co-Secant. 

...Co. Sine. 

...Sine. 

2) 
...Sine. = 



Long, in Time. 



Time 


H. 


Chronometer, ®'g Altitude. 

M. S. o 


3) 




3) : 


Mean 
Correction 





: : Mean. : : 
: : SemidiamPar. -f- 


Time at G. 


: : ®'s App. Alt. : : 
Dip. Ref. 


© T s dec. noon. 
Varia. 


: : @'s Cor. Alt. : : 


Declin. 
Polar Dist. 




: 


®'s cor. alt. 
Lat. 
Polar dist. 

Sum. 


o 


: : Sedant. 

: Co. Secant. 


Half Sum. 
@'s alt. sub. 




; : Co. Sine. 


Remainder. 




: : Sine. 




H. 


2) ' 


Appar. time. 
Equation. 


: : Sine. = 


Mean time at 
Ship, 
at G. 




. , „ a ' * 


Long, in Time. 







Time per Chronometer. 

H. M. S. 



%\ Altitude, 



3) 


3) : 




Mean : 
Correction : 


: Mean. 

: Semidiam Par. + 


: 


Time at G. 

O ' 


: ®'a App. Alt. : 
Dip. Ref. : 




©'a dec. noon 
Varia. 


0'i Cor. Alt. : 




Declin. 

Polar Dist. : 






O ' 

©'s cor. ah. : 
Lat. : 
Polar dist. 


: Secant. 

Co. Secant. 




Sum. : 






Halt Sum. : 
©'a alt. sub. : 


: Co. Sine. 




Remainder. : 


: Sine- 




H. M. 

Appar. time. : 
Equation. 

Mean time at 
Ship, 
at G. 

Long, in Time. : 


2) ' 




Sine. = 







Turn' 


pei < ' 


tironometei 

M. 


Altitude 


3) 


3) : 


Mean 
Correction 






Mean. : : 
Semidiam Par. -f" 


Time at G. 


o 





©'s App. Alt. : : 
Dip. Ref. 


©'s dec. noon. 
Varia. 

Declin. 
Polar Dist. 


®'s Cor. Alt. : : 


©'s cor. alt. 
Lat. 
Polar dist. 

Sum. 


o 


__ 


Secant. 

Co. Secant. 


Half Sum. 
@'s alt. sub. 


» 




Co. Sine. 


Remainder. 


: 




Sine. 




H. 


M. S. 


2) 


Appar. time, 
Equation. 


Sine. = 


Mean time at 
Ship, 
at G. 


: 




O ' i* 


Long, in Time. 






■a : : 



Time per C 

H. 


hronometer. 

M. S. 


©'a Altitude. 


3) 






3) : 


Mean 
Correction 


: 


: 


Mean. - : 
Semidiam Par. + 


Time at G. 


/ 


" 


©>s App. Alt. : 

Dip. Ref. : : 


©'9 dec. noon 
Varia. 


©'i Cor. Alt. : : 


Declin. 
Polar Dist. 


: 








©'s cor. alt. 
Lat. 
Polar dist. 


' 


tf 


Secant. 

... ....Co. Secant. 


Sum. : : 


Half Sum. 
©'s alt. sub. 


: 


: 


»Co. Sine. 


Remainder. 


: 




Sine- 


H. 

Appar. time. 
Equation. 


M. 


s. 


2) ' 
Sine. = ' 


Mean time at 
Ship. 
atG. 


: 


: 


o ' • * 


Long, in Time. 


: 


: 


s== t • 



Time per 

H. 


Chronometer. ©'■ Altitude. 

M. 3. ° ' " 


3) • 




3) : 


Mean 
Correction : 




: Mean. : : 
: Semidiam Par. + 


Time at G. : 

o 


/ 


©'s App. Alt. 

Dip. Ref. 

// 


©'s dec. noon : 
Varia. 

Declin. J 
Polar Dist. 


: ©'s Cor. Alt. : ; 




©'s cor. alt. 
Lat. : 
Polar dist. : 


/ 


n 

: Secant. 

: .......Co. Secant. . 


Sum. : 






Half Sum. : 
©'s alt. sub. : 




: ...... .Co. Sine. 


Remainder. : 




: Sine. ' 


H. 

Appar. time. 
Equation. 


M. 


2) ' 
: Sine. = ' 


Mean time at 
Ship, 
at G. 




_ . .. o ' it 


Long, in Time. 


1 


i =* : : 



Time 


per Chronometer 

H. M. s. 


©'s Altitude 

' " 


3) 




3) : 


Mean. 
Correction 


: 


Mean. : 
Semidiam Par. + 


Time at G. 


O ' " 


© App. Alt. ; : 
Dip. Ref. : 


@'s dec. noon 
Varia. 


®'s Cor. Alt. : 


Declin. 
Polar Dist. 


: 




®'s cor/alt. 
Lat. 
Polar dist. 


o ' " 


Secant. 

Co-Secam 


Sum. 

Half Sum. 
©'s alt. sub. 

Remainder. 





........Co. Sine. 

Sine. 




H. M. S. 


2) 


Appar. time. 
Equation. 


Sine. = 


Mean time at 
Ship. 
atG. 




o ' " 


Long, in Time. 




= : : 



Time per 

IT 


Chronometer 

M S. 


<£'s Altitude. 

O ' li 


3) 




3) : 


Mean 
Correction : 




Mean. : : 
Semidiam Par. + 


Time atG. 

o 


t n 


©'s App. Alt. : 

Dip. Ref. : : 


®'s dec. noon 
Varia. 


©'a Cor. Alt. : : 


Declin. : 
Polar Dist. 


: 




o 
© 's cor. alt. : 
Lat. : 
Polar dist. : 


/ " 


Secant. 

Co. Secant. . 


Sum. : 






Half Sum. 
®'s alt. sub. : 


: 


Co. Sine. 


Remainder. 


: 


Sine. ' 




M. S. 


2) ' 


Appar. time. : 
Equation. : 


Sine. = ' 


Mean time at : 
Ship. 
atG- : 


: 


o * // 


Long, in Time. i 







Time per Chronometer 



tg's Altitude. 



3) 






3) 


: 




Mean. 
Correction 


: 




Mean. 
Semidiam Par. 


+ 


' 


Time at G. 


o 


' 


: © App. Alt. 
Dip. Ref. 


; 


: 


@'s dec. noon 
Varia. 


©'s Cor. Alt. 


• 


: 


Declin. 
Polar Dist. 










@'s cor. alt. 
Lat. 
Polar dist. 


o 


' 


: Secant. 

: Co-Secant. 




Sum. 

Half Sum. 
Q'a alt. sub. 







: Co. Sine. 




Remainder. 


H. 


M. 


: Sine. 

2) 
s. — 
Sine. = 






' 




Appar. time. 
Equation. 


' 




Mean time at 
Ship. 
atG. 


: 




: 


H 



Long, in Time. 



Time per Chronometei . 
h. m. a 



O'd Altitude 



3) 



Mean 
Correction 

Time at G. 



&'s dec. noon. 
Varia. 

Declin. 
Polar Dist 



3) : 


Mean. 
Semidiam Par. 


+ 


©'a App. Alt. 
Dip. Ref. 





fl's Cor. Alt. 



©*s cor. alt. 
Lat. 
Polar dist. 



.Secant. 
.Co. Secant. 



Sum. 

Half Sum. 
@'s alt. sub. 

Remainder. 



Appar. time. 
Equation. 

Mean time at 
Ship, 
at G. 

Long, in Time. 



.Co. Sine. 



Sine. 



2) ' 



.Sine. 



Time per Chronometer 

H. M. S. 



©>S Altitude . 



3) 






3) : 


Mean 
Correction 






: Mean. ■ : 
: Semidi&m Par. ~f- 


Time at G. 





' 


©>s App. Alt. : : 
Dip. Ref. : : 


®'s dec. noon 
Varia. 


©'a Cor. Alt. 


Declin. 
Polar Dist. 








@ ? s cor. alt. 
Lat. 
Polar dist. 


o 




: ........Secant, 

: Co. Secant. 


Sum. 








Half Sum. 
©'a alt. sub. 






: .. Co. Sine. 


Remainder. 






c Sine- 


Appar. time. 


H. 


M. 


2) ' 
: Sine. = 



Equation. 



Mean time at 
Ship. 
atG. 

Long, in Time. 



Time per Chronometei . 

M M 



Altitude 



3) 



3) 



Mean 
Correction 

Time at G. 



ys dec. noon. 
Varia. 



Mean. : 

SemidiamPar. -j- 



©'s App. Alt. 
Dip. Ref. 

Q'a Cor. Alt. 



Declin. 
Polar Dist. 



©'s cor. alt. : 
Lat. : 
Polar dist. 

Sum. : 


Secant. 

: Co. Secant. 


Half Sum. ; 
©'s alt. sub. : 


Co. Sine. 


Remainder. : 


Sine. 



2) ' 



Appar. time. 
Equation. 



.Sine. 



Mean time at 
Ship. 
atG. 



Long, in Time, 



Tiiue per Chronometer. 

H. M. 8. 



I's Altitude. 



3) 


3) : 




Mean 
Correction 


: : Mean. : 
Semidiam Par. + 


J 


Time at G. 




: @'s App. Alt. 

Dip. Ref. : 


: 


®'s dec. noon 
Varia. 


: : @'s Cor. Alt. : 




Declin. 
Polar Dist. 








©'s cor. alt. : 
Lat. 
Polar dist. : 


i n 

: Secant* 

... ....Co. Secant. 




Sum. 






Half Sum. 

©'s alt. sub. : 


: Co. Sine, 




Remainder. 


Sine- 




H. 


2) ' 

jyj S „. 




Appar. time. : 
Equation. 

Mean time at 

Ship. : 
atG. 

Long, in Time. 


: Sine. = 


H 



Tune per 

H. 


Chronometer . 

M. S. 


<$'s Altitude. 


3) : 






3) : 


Mean : 
Correction : 




: 


Mean. : 
Semidiam Par. + 


Time at G. : 


/ 


n 


@'s App. Alt. 

Dip. Ref. : : 


©*s dec. noon 
Varia. 


@'s Cor. Alt. 


Declin. : 
Polar Dist. 




: 




o 
®'s cor. alt. 

Lat. : 
Polar dist. : 


/ 


t> 


Secant. 

Co. Secant. . 


Sum. : 








Half Sum. : 
®'s alt. sub. : 






Co. Sine. 


Remainder. : 




: 


Sine. 


H. 

Appar. time. 
Equation. 


M. 


s. 


2) ' 
Sine. = ' 


Mean time at 
Ship. 
atG. 




» 


o ' » 


Long, in Time. 









Time per Chronometer 



©'s Altitude. 



3) 








3) 






Mean. 
Correction 


: 




Mean. 
Semidiam Par. 


+ 


: 


Time at G. 


o 


' 


" 


© App. Alt. 
Dip. Ref. 


; 




@'s dec. noon 
Varia. 


$'s Cor. Alt. 

Secant. 

Co-Secant. 




' ■ 


Declin. 
Polar Dist. 




: 






©'s cor/alt. 
Lat. 
Polar dist. 


o 


' 


" 




Sum. 

Half Sum. 
© 7 s alt. sub. 

Remainder. 


H. 


M. 


S. 


Co. Sine. 

Sine. 






2) 


• 




Appar. time. 
Equation. 


Sine. = 







Mean time at 
Ship. 
atG. 



Long, in Time, 



Turn per Chronometer. 

H. M. S. 



©*ti Altitude. 



3) : 



Mean 
Correction 

Time at G. 



©'a dec. noon 
Varia. 

Declin. 
Polar Dist, 



3) 



o ' " 



Mean. : 

Semidiam Par. + 



©'s App. Alt. 
Dip. Ref. 

#'s Cor. Alt. 



©'a cor. alt. 
Lat. 
Polar dist. 

Sum. 

Half Sum. 
©'s alt. sub. 



Remainder. 



Appar. time. 
Equation. 

Mean time at 
Ship. 
atG, 



.Secant. 

..Co. Secant. . 

..Co. Sine. 



..Sine, 



2) ' 



..Sine. = 



Long, in Time. 



Time per Chronometer 
h. m. s. 



$*■ Altitude. 



3) 






• 


3) : 




Mean. 
Correction 


: 




: 


Mean. : : 
Semidiam Par. + 




Time at G. 





/ 


- 


& App. Alt. ; : 
Dip. Ref. : : 




©'s dec. noon 
Varia. 


®'s Cor. Alt. : : 

Secant. 

Co-Secant. 

Co. Sine. 

Sine. 




Declin. 
Polar Dist. 










®'s cor. alt. 
Lat. 
Polar dist. 


o 


' 


" 




Sum. 


: 








Half Sum. 
®'s alt. sub. 

Remainder. 


H. 


M. 


S. 






2) 




Appar. time. 
Equation. 

Mean time at 
Ship. 
atG. 


Sine. = 


ft 



Long, in Time. 



Time per Chronometei . 

h. m. s. 



JJ'g Altitude. 



3) 



Mean 
Correction 

Time at G. 



©'s dec. noon. 
Varia. 

Declin. 
Polar Dist. 



§>'s Cor. Alt. 



3) : 


Mean. 
SemidiamPar. 


+ 


®'s App. Alt. 
Dip. Ref. 


: 



©*s cor. alt. 
Lat. 
Polar dist. 

Sum. 

Half Sum. 
@'s alt. sub. 

Remainder. 



Appar. time. 
Equation. 

Mean time at 
Ship, 
at G. 

Long, in Time. 



.Secant. 
.Co. Secant, 

.Co. Sine. 
..Sine. 

..Sine. = 



Time per Chronometer. 
h. m. s. 



^s Altitude. 



3) 



Mean 

Correction 

Time at G. 



H^s dec. noon 
Varia. 

Declin. 
Polar Dist. 



3) : 


Mean. 
Semidiam Par. 


+ 


i's App. Alt. 

Dip. Ref. : : 



@'s Cor. Alt. 



©'s cor. alt. 
Lat. 
Polar dist. 

Sum. 

Half Sum. 
©'a alt. sub. 

Remainder. 



Appar. time. 
Equation. 



.secant, 

,Co. Secant. 

Co. Sine. 

Sine- 

Sine. = 



Mean time at 
Ship. 
atG. 



Long, in Time. 



Time 


pei 

H. 


Chronometei 




Altitude. 


3) 






3) 




Mean 
Correction 


O 


, 


Mean. 
Semidiam Par. 


+ 


Time at G. 


©'sApp.Alt. 
Dip. Ref. 


: 


©'s dec. noon. 
Varia. 

Declin. 
Polar Dist. 


@'s Cor. Alt. 




©'s cor. alt. 
Lat. 
Polar dist. 

Sum. 


O 


LL 


Secant. 

Co. Secant, 

Co. Sine. 

Sine. 




Half Sum. 
@'s alt. sub. 




; ; 




Remainder. 


H. 


M. S. 


r 




2) 


t 


Appar. time. 
Equation. 


Sine. = 


' 


Mean time at 
Ship, 
at G. 




: : 


' * 


Long, in Time. 






: : 



Time per Chronometer. 

H. M. S. 



©'s Altitude. 



3) 



Mean 
Correction 

Time at G. 



©'a dec. noon 
Varia. 



3) 



Mean. : 

Semidiam Par. + 



®'s App. Alt. 
Dip. Ref. 

(ft'i Cor. Alt. 



Declin. 
Polar Dist. 








©>s cor. alt. 
Lat. 
Polar dist. 





/ // 


....Secant. 
....Co. Secant 


Sum. 








Half Sum. 
©'s alt. sub 


: 


: 


....Co. Sine, 


Remainder. 


H. 




....Sine- 


Appar. time. 
Equation. 

Mean time at 
Ship. 
atG. 


M. S. 


2) 
....Sine. 


Long, in Time 


• 


; 


b= 



Time per 

H. 


Chronometer. 
M. s. 


®'s Altitude. 

O ' // 


3) 




3) : 


Mean 
Correction 


: 


Mean. 

Semidiam Par. + 


Time at G. 


t ir 


©'s App. Alt. : : 
Dip. Ref. : : 


0's dec. noon 
Varia. 


#'s Cor. Alt. : 


Declin. 
Polar Dist. 


: 




o 

® f a cor. alt. 
Lat. 
Polar dist. 


/ " 


Secant. 

....... Co. Secant. . 


Sum. 






Half Sum. 
®'s alt. sub. 


: 


Co. Sine. 


Remainder. 


: : 


Sine. 




M. S. 


*> 


H. 

Appar. time. 
Equation. 

Mean time at 
Ship. 
atG. 


.Sine. = ' 

o • ft 


Long, in Time. 


1 


— : : 



pei Chronometer 

h. m. s. 



*»s Altitude >. 






Mean 
Correction 

Time at G. 



®'s dec. noon 
Varia. 

Declin. 
Polar Dist. 



Mean. 

Semidi&m Par. + 



®'s App. Alt. 
Dip. Ref. 

Q'i Cor. Alt. 



| 5 s cor. alt. 
Lat. 

Polar dist. 

Sum. 

Half Sum. 
®'s alt. sub. 



Remainder. 



Appar. time. 
Equation. 

Mean time at 
Ship. 
atG. 

Long, in Time* 



.....Secant. 
....Co. Secant. 



.Co. Sine, 



.bine- 



2) 



.Sine. 



'1 inn* 


per < 


Ihronomi Altitude 


3) 


3) : 


Mean 
Correction 


o 


: Mean. : : 
Semidiam Par. -j- 


Time at G. 


: ©'s App. Alt. : : 
Dip. Ref. 


@'s dec. noon. 
Varia. 


: © ? s Cor. Alt. : 


Declin. 
Polar Dist. 






@'s cor. alt. 
Lat. 
Polar dist. 

Sum. 


o 


: Secant. 

Co. Secant. 


Half Sum. 
@'s alt. sub. 


5 


: Co. Sine. 


Remainder. 


H. 


: Sine. 




2) ■ 


Appar. time. 
Equation. 


: Sine. = 


Mean time at 
Ship. 
atG. 


: 


> ' * 


Long, in Time. 







Time per Chronometer. 

H. M. S. 



Altitude 



3) 



Mean 
Correction 

Time at G. 



®'s dec. noon 
Varia. 

Declin. 
Polar Dist, 



3) 



Mean. 

Semidiam Par. + 



App. Alt. 
Dip. Ref. 

@'s Cor. Alt. 



@'s cor. ait. 
Lat. 
Polar dist. 

Sum. 

Half Sum. 
®'s alt. sub. 

Remainder. 



Appar. time. 
Equation. 

Mean time at 
Ship. 
atG. 



H. M. 



Secant. 

Co. Secant. 

Co. Sine. 

.Sine- 

2) 
s. — 
Sine. = 



Long, in Time. 



Time pei ( !hron< 

B. M 



\ Ititude. 





) : : 3) 






Mean 
Correction 


: : Mean. 

: *• Semidiam Par. 


+ 




Time at G. 


: ®'s App. Alt. 
Dip. Ref. 






©'s dec. noon 
Varia. 


: : Cor. Alt. 






Declin. 








Polar Dist. 








©*3 cor. alt. 


O ' " 






Lat. 
Polar dist. 


: : Secant. 

: Co. Secant. 






Sum. 








Half Sum. 
® T s alt. sub. 


; : Co. Sine. 


r 




Remainder. 


• : Sine. 






2) 

H. M. s 


/ 




Appar. time. 
Equation. 


: : Sine. = 






Mean time at 






Ship. 
atG. 








Long, in Time 







LIB**" °'^!tf\\ 



i i ;,/• j : i ( hronometei • 

H. ^1 S. 






Mean 

clioQ 

Time at G. 



©'s dec. noon 
\ aria. 

Declin. 
Polar Dist. 




V W3 5* 1 »* 7 * 



3) 






Moan. 
Semidi&m Par. 


+ 




kpp. Alt. : 
Dip. Kef. : 



®'iCor. Alt. 



©'s cor. alt. 
Lat. 
Polar dist. 

Sum. 

Half Sum. 
©'s alt. sub. 



Remainder. 



Appar. time. 
Equation. 

Mean time at 
Ship. 
atG. 



Sccaut. 

Co. Secant. 



M. S. 



,Co. Sine. 

.Sine- 

2) 
.Sine. = 



Long, in Time. 



